Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic97 | C2 | semidirect |
| 3. #20260642 | C2 | semidirect |
| 5. #20260628 | C2 | semidirect |
| 6. #20260610 | C2 | semidirect |
| 7. #20260605 | C2 | semidirect |
| 8. #20260581 | C2 | semidirect |
| 27. #124×C97 | C4 | semidirect |
| 49. C2×Q8×C97 | C2×C4 | semidirect |
| 56. C22⋊C4×C97 | C2×C4 | semidirect |
| 57. C42×C97 | C2×C4 | semidirect |
| 112. C97 | #2326 | semidirect |
| 125. #124 | Dic97 | semidirect |
| 145. C2×Q8 | C2×Dic97 | semidirect |
| 165. C22⋊C4 | C2×Dic97 | semidirect |
| 169. C42 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic97 | 2 |
| C2×D4×Dic97 | 2 |
| #20260642 | 2 |
| #20260638 | 2 |
| #20260628 | 2 |
| #20260610 | 2 |
| #20260605 | 2 |
| #20260581 | 2 |
| C2×#124×C97 | 2 |
| #2326 | 97 |